Simple crosstabs (also
called cross tabulation, or contingency tables), which examine the influence
of one variable on another, should be only the first step in the analysis
of social science data. It is fun to hypothesize that the more conservative
a person's political orientation, the more likely they are to oppose abortion,
run the crosstabs, and then conclude you were right. However, this one-step
method of hypothesis testing is very limited. What if all the Republicans
in your sample are religiously conservative and all the Democrats are atheists?
Is it political party that best explains your findings, or is it religious
orientation? Or what if the political conservatives as a group are much
older than the liberals, would age then be the real causal factor? Or is
it some combination among all of these variables that explains the varying
opinions of your respondents? Or suppose you hypothesize that men and women
differed significantly in their belief that the ability to think for one's
self (GSS98A.SAV variable name = THNKSELF) was an important value to instill
in children. The crosstabs for THNKSELF and SEX show that while a slight
majority (51%) of all respondents reported that this was the most important
value among those listed (to be popular, to obey, to help others, to work
hard), only 45% of the men surveyed agreed with this compared with 57%
of the women (see Figure 8-1).
Figure 8-1
This percentage point difference
(epsilon) of 12 is "interesting," even if you don't yet know whether it
is statistically significant. Can you conclude that gender is the causal
factor here? While it may indeed be true that gender is explanatory, you
won't really know this until you have failed to account for this variation
in any other way. To do this, run crosstabs of (i.e., "control for") other
independent variables to see if something else might account for this variation
among respondents.
Recall that your original crosstabs
procedure produces one contingency table, with as many rows as there are
categories (or values) of the dependent variable, and as many columns as
there are categories of the independent variable. So in Figure 8-1, we
have a 5 by 2 table. When you start using control (sometimes called test)
variables, you will get as many separate tables as there are categories
of the control variable. For instance, if you want to control for levels
of education, and simply used EDUC as the control variable, you end up
with 20 separate tables. This is NOT a good idea. Try doing this to see
what we mean. Notice how difficult it is to compare across this many tables.
So before you do any further analysis, recode your variables into the smallest
number of categories that are still logically useful.
In this next example EDUC was
recoded as EDUC2 into three categories (0-11 years, 12 years, more than
12 years). After you have done these recodes, let's see what happens when
we do crosstabs again, this time controlling for education. To do the appropriate
crosstabs, go to the Analyze, Descriptive Statistics, Crosstabs menu and
double-click. Enter THNKSELF into the Row box and SEX into the Column box.
(Recall that this is how you generate one contingency table.) Now you are
ready for the next step, the addition of a control variable. Choose EDUC2
from your variables list and enter it into the empty box at the bottom
of the Crosstabs screen. Figure 8-2 shows you what this will look like.
Figure 8-2
The SPSS output for this procedure
is shown in Figure 8-3.
Figure 8-3
Note that there are now three
tables, one for each value of EDUC2. If you want to produce more three-way
tables, just move the variables from the variable list into that third
box.
Figure 8-1 shows the
original, or zero-order contingency table of the relationship between THNKSELF
(unrecoded) and SEX.
Figure 8-3 shows the three partial
tables that resulted from THNKSELF crosstabbed by SEX, controlling for
EDUCR.
First, note that there is a big
difference among respondents at each of the three educational levels. Only
a third (34%) of the respondents with less than a high school education
thought that thinking for oneself was the most important value to instill
in children. Compare this with the three out of five (61%) with 13 or more
years of education who did think this was most important. Also note that
as education increases, women are more likely than men to say that thinking
for oneself is the most important value. It appears here that educational
level seems to explain more than does gender. Try other variables as a
control to see what happens. As a general rule, here is how to interpret
what you find from this elaboration analysis:
-
If the partial tables are similar
to the zero-order table, you have replicated your original findings, which
means that in spite of the introduction of a particular control variable,
the original relationship persists. The only way to convince us that this
is indeed a strong, or even causal, relationship is if you control for
all the other logical independent variables you can think of, and still
find essentially no differences between the zero-order tables and their
partials.
-
If all the partials are significantly
less than those found in the original AND IF your control variable is antecedent
(occurs prior in time) to both the other variables, you have found a spurious
relationship and explained away the original. In other words, the original
relationship was due to the influence of that other variable, not the one
you hypothesized.
-
If the partials are less AND IF
your control variable is intervening, you have interpreted the relationship.
If the time sequence between the independent and control variable is not
determinable (or otherwise unclear), you don't know whether you have explanation
or interpretation, but you do know that the control variable is important.
-
If one or more partials is stronger
than the original relationship and one or more is weaker, you have discovered
the conditions under which the original relationship is strongest. This
is referred to as specification, or the interaction effect.
-
If the zero order table showed weak
association between the variables, you might still find strong associations
in the partials (which is a good argument for keeping on with your initial
analysis of the data even if you didn't "find" anything with bivariate
analysis). The addition of your control variable showed it to have been
acting as a suppressor in the original table.
-
Last, if a zero order table shows
only a weak or moderate association, the partials might show the opposite
relationship, due to the presence of a distorter variable.
Try some of your own three-way (or
higher) tables using some of the data sets we have provided you with. Recall
that for this procedure, there should be few categories for each variable,
particularly your control variables (so you might need to recode), and
you are limited to variables measured at, or recoded to, nominal or ordinal
levels.
Multiple Regression
Once you have discovered that several
of your independent variables are related to your dependent variable, you
might want to try multiple regression (multiple linear regression analysis).
The three-or-more-way crosstabs shown previously are more an exploratory
technique, whereas multiple regression is more explanatory. With multiple
regression you can generate beta values (partial regression coefficients)
which give you an idea of the relative impact of each independent variable
on the dependent.
You also will generate the R-squared
value, which is a summary statistic of the impacts of all the independent
variables taken together. Remember the important assumptions for using
regression: a linear relationship between each independent variable and
the dependent; a normal distribution of your variables, and variables measured
at interval or ratio levels.
Go to the Analyze, Regression,
Linear menu. For your dependent variable, choose THNKSELF from the variable
list. For the independent variables choose EDUC (unrecoded), ATTEND, BIBLE,
and SEX (see Figure 8-4).
Figure 8-4
Note that EDUC doesn't show up
in the list of independent variables, but you could use the scroll bar
to find it. Now choose the "Statistics" button at the bottom of the dialog
box and a new dialog box will appear, shown here in Figure 8-5 with the
default options.
Figure 8-5
Click on the "Continue" button
to return to Figure 8-5, then click on the "Plots" button. Your screen
should now look like Figure 8-6.
Figure 8-6
Click on "Continue" and look
at your next choice, which is "Save." A dialog box like Figure 8-7 appears.
Figure 8-7
Click on "Continue" and then
"Options" and your screen should look like Figure 8-8, which shows the
default options (then click "Continue" to return to the Linear Regression
dialog box).
Figure 8-8
Your last task is to choose your
method of analysis. In Figure 8-4 you will see the "Method:" button right
under the "Independent(s): " box. You have several choices here, and you
can use the scroll button to see what they are. "Stepwise" is the one we
chose for this example, and the one that you will probably use most often.
(See Figure 8-9.) For an in-depth discussion of all the possible choices
for Multiple Regression, you will need to consult the SPSS manuals.
Figure 8-9
Figure 8-10 shows you the first
screen of the results in the Output window when you finally click "OK"
in the Linear Regression dialog box after having chosen stepwise regression
using all the default options.
Figure 8-10